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Truncated Lévy process with scale-invariant behavior

Author

Listed:
  • Ivanov, Plamen Ch.
  • Podobnik, Boris
  • Lee, Youngki
  • Stanley, H.Eugene

Abstract

We develop a scale-invariant truncated Lévy (STL) process to describe physical systems characterized by correlated stochastic variables. The STL process exhibits Lévy stability for the probability density, and hence shows scaling properties (as observed in empirical data); it has the advantage that all moments are finite (and so accounts for the empirical scaling of the moments). To test the potential utility of the STL process, we analyze financial data.

Suggested Citation

  • Ivanov, Plamen Ch. & Podobnik, Boris & Lee, Youngki & Stanley, H.Eugene, 2001. "Truncated Lévy process with scale-invariant behavior," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 154-160.
    • Handle: RePEc:eee:phsmap:v:299:y:2001:i:1:p:154-160
    DOI: 10.1016/S0378-4371(01)00290-4
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    Cited by:

    1. Sun, Qi & Xu, Weidong, 2015. "Pricing foreign equity option with stochastic volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 437(C), pages 89-100.
    2. Chang, Lo-Bin & Geman, Stuart, 2013. "Empirical scaling laws and the aggregation of non-stationary data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(20), pages 5046-5052.
    3. Stanley, H. Eugene & Plerou, Vasiliki & Gabaix, Xavier, 2008. "A statistical physics view of financial fluctuations: Evidence for scaling and universality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(15), pages 3967-3981.
    4. Sandoval, Leonidas & Franca, Italo De Paula, 2012. "Correlation of financial markets in times of crisis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(1), pages 187-208.
    5. Kang, Sang Hoon & Yoon, Seong-Min, 2007. "Long memory properties in return and volatility: Evidence from the Korean stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 385(2), pages 591-600.
    6. Yu, Jianfeng & Xu, Weidong, 2016. "Pricing turbo warrants under mixed-exponential jump diffusion model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 451(C), pages 490-501.

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